It proposes that the Commons would hold a vote on the deal on November 27 after a week in which the Government would line up business leaders, foreign politicians and Westminster insiders to publicly endorse Ms May's plan.

Ministers will adopt a tone of "measured success" but there will be no "champagne corks popping", it claims.

However, Downing Street dismissed the document, saying it "doesn't represent the Government's thinking". It highlighted the "childish language", including a misspelling of Irish premier Leo Varadkar's name.

It states: "Trying to get Varadker to support."

A Government spokesperson said: "The misspelling and childish language in this document should be enough to make clear it doesn't represent the Government's thinking. You would expect the Government to have plans for all situations - to be clear, this isn't one of them."

The plan suggests the deal should have been agreed by the Cabinet yesterday. Dominic Raab, the Brexit Secretary, would then have announced a "moment of decisive progress" tomorrow.

Instead, leaders in both the UK and Brussels warned that a deal was not close, and a three-hour meeting of the Cabinet resulted in no decisions being made. A second meeting is likely to be held later in the week.

According to the document, No 10 officials are planning a cautious response if a deal is finally agreed.

"The narrative is going to be measured success, that this is good for everyone, but won't be all champagne corks popping," it says.

The plan suggests Mrs May would give a speech at the Confederation of British Industry conference on November 19 at which she would say "we have delivered on the referendum". The Prime Minister would argue that "this deal brings the country back together, now is the time for us all to unite behind it for the good of all our futures".

This would be followed by a week of focus on the content of the deal, with each day dedicated to a particular issue, including the economy, immigration and "global Britain".

Business leaders and foreign dignitaries, including the Prime Minister of Japan, would be lined up to publicly support the deal. The mayor of Manchester, Labour's Andy Burnham, is mentioned as another potential backer.

Mrs May would also do an interview with BBC presenter David Dimbleby. The deal would be introduced in Parliament on November 19 and voted on by MPs on November 27.

Of that day, the document says: "Evening is the vote. HISTORIC MOMENT, PUT YOUR OWN INTERESTS ASIDE, PUT THE COUNTRY'S INTERESTS FIRST AND BACK THIS DEAL."

Earlier, it was reported that the Government is drawing up new proposals for a "review mechanism", to allow the UK to escape any backstop arrangement if talks on a trade deal break down.

Mrs May is thought to regard the idea as a means of allaying the concerns of Conservative and DUP MPs that Britain could be permanently trapped in a customs union with the EU as part of arrangements to avoid a hard border in Ireland.

Sources close to talks said London regarded it as a "big step" that the EU side now appears ready to contemplate a means for bringing the backstop to an end short of a broader trade treaty.

The Prime Minister said that she wanted to reach a withdrawal agreement as soon as possible, but "not at any cost".

A gathering of EU leaders in Brussels on the previously mooted date of November 17 is now thought to have been ruled out, while a special summit later in the month would be dependent on EU negotiator Michel Barnier declaring that "decisive progress" has been made in talks.

But Mr Barnier himself said a breakthrough on the Irish border issue was not close.

He said: "There is still a real point of divergence on the way of guaranteeing peace in Ireland, that there are no borders in Ireland, while protecting the integrity of the single market."